Problem: Solve for $x$ and $y$ using elimination. ${-x-2y = -11}$ ${3x-3y = -3}$
Answer: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the top equation by $3$ ${-3x-6y = -33}$ $3x-3y = -3$ Add the top and bottom equations together. $-9y = -36$ $\dfrac{-9y}{{-9}} = \dfrac{-36}{{-9}}$ ${y = 4}$ Now that you know ${y = 4}$ , plug it back into $\thinspace {-x-2y = -11}\thinspace$ to find $x$ ${-x - 2}{(4)}{= -11}$ $-x-8 = -11$ $-x-8{+8} = -11{+8}$ $-x = -3$ $\dfrac{-x}{{-1}} = \dfrac{-3}{{-1}}$ ${x = 3}$ You can also plug ${y = 4}$ into $\thinspace {3x-3y = -3}\thinspace$ and get the same answer for $x$ : ${3x - 3}{(4)}{= -3}$ ${x = 3}$